Performance measure of multiple-channel queueing systems with imprecise data using graded mean integration for trapezoidal and hexagonal fuzzy numbers

Zeina Mueen; Nerda Zura Zaibidi; Razamin Ramli

doi:10.32890/jcia2022.1.2.1

Authors

Zeina Mueen University of Baghdad, Iraq
Nerda Zura Zaibidi Universiti Utara Malaysia, Malaysia https://orcid.org/0000-0002-7312-144X (unauthenticated)
Razamin Ramli Universiti Utara Malaysia, Malaysia https://orcid.org/0000-0002-0445-9033 (unauthenticated)

DOI:

https://doi.org/10.32890/jcia2022.1.2.1

Keywords:

fuzzy numbers, graded mean integration, multiple channel queueing model, performance measures, two class of arrivals

Abstract

In this paper, a procedure to establish the different performance measures in terms of crisp value is proposed for two classes of arrivals and multiple channel queueing models, where both arrival and service rate are fuzzy numbers. The main idea is to convert the arrival rates and service rates under fuzzy queues into crisp queues by using graded mean integration approach, which can be represented as median rule number. Hence, we apply the crisp values obtained to establish the performance measure of conventional multiple queueing models. This procedure has shown its effectiveness when incorporated with many types of membership functions in solving queuing problems. Two numerical illustrations are presented to determine the validity of the procedure in this queueing model, which involved using trapezoidal and hexagonal fuzzy numbers. It can be concluded that graded mean integration approach is efficient with fuzzy queueing models to convert fuzzy queues into crisp queues. This finding has contributed to the body of knowledge by suggesting a new procedure of defuzzification as another efficient alternative.

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